A367062 G.f. satisfies A(x) = 1 + x*A(x)^3 + x^3*A(x)^6.

1, 1, 3, 13, 64, 339, 1889, 10917, 64836, 393292, 2426335, 15176847, 96029114, 613540477, 3952727925, 25649572693, 167494312692, 1099850119488, 7257905610260, 48106858236044, 320131295055690, 2138010763838375, 14325505944147495, 96273042489762471

Offset: 0

Author

Seiichi Manyama, Nov 04 2023

Keywords

• nonn

Crossrefs

Cf. A366676, A367057, A367058, A367059, A367060, A367061.

Programs

PARI

a(n) = sum(k=0, n\3, binomial(2*n+1, k)*binomial(3*n-3*k, n-3*k))/(2*n+1);

Formula

a(n) = (1/(2*n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+1,k) * binomial(3*n-3*k,n-3*k).